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Ex 3.3, 12 - Prove that sin2 6x - sin2 4x = sin⁡2x sin⁡10x - (x + y) formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex 3.3, 12 Prove that sin2 6𝑥 – sin2 4𝑥 = sin⁡2𝑥 sin⁡10𝑥 Solving L.H.S. sin2 6x – sin2 4x Using a2 – b2 = (a + b) (a - b) = (sin 6x + sin 4x) (sin 6x – sin 4x) Lets calculate (sin 6x + sin 4x) and (sin 6x – sin 4x) separately Hence sin2 6x – sin2 4x = (sin 6x + sin 4x) (sin 6x – sin 4x) = (2 sin 5x cos x) (2 cos 5x sin x) = (2 sin 5x cos 5x) . (2 sin x cos x) = (sin 10x) × (sin 2x) = R.H.S. Hence, L.H.S. = R.H.S. Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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